Date Awarded


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)


Applied Science


Leah B Shaw


The spread of diseases and opinions has profoundly affected the development of human societies. The structure of the underlying social network may change as a result of individuals changing their social connections in response to an ongoing epidemic or opinion spreading, either for self protection or as an expression of personal values. The interaction of spreading processes and the underlying network structure has been a focus of many recent studies. In this dissertation, we construct models to better incorporate heterogeneous responses to disease spread and attempted opinion spread.;We first model the simultaneous spread of an epidemic and awareness about the epidemic on an adaptive social network. A previous Susceptible-Infectious-Susceptible (SIS) model with avoidance rewiring is extended. Susceptible and infectious nodes are each divided into aware and unaware types. Aware nodes affect the network structure by rewiring their connections to reduce disease exposure. Public media information is considered as an external source of node awareness. The effects of awareness on disease spread and network structure are explored using stochastic simulations and mean field equations. Network adaptation can generate steady state behavior or periodic oscillations. The epidemic threshold is predicted using two methods that improve upon mean field predictions, and a critical media rate controlling the existence of an epidemic threshold under fast rewiring is given.;Node-to-node communication is then introduced as another source of node awareness, and its influence on disease levels and epidemic thresholds is compared with public media information. A relationship of the thresholds under different awareness sources is derived. Our results in both models indicate that node awareness can play a significant role in minimizing disease spread, and in some cases media information is more effective at controlling disease than communication.;We also model the competition of two opinions on a social network. A small fraction of committed supporters of a new opinion is randomly distributed in the network among supporters of a previous opinion. We introduce a new process, exacerbation, in which committed supporters of an opinion may drive their contacts away from that opinion and toward strong commitment to the opposing viewpoint. In addition to network simulations, a mass action model of the process is studied. We find that exacerbation can change the final outcome of opinion competition. The influence of the initial fraction committed to the new opinion is also explored.



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